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| United States Patent |
5,189,357
|
|
Woodson
, et al.
|
February 23, 1993
|
Method and apparatus for improving performance of AC machines
Abstract
A method and apparatus for improving the performance of polyphase AC
machines. The polyphase AC machines are excited both with a fundamental
frequency and with an odd harmonic of the fundamental frequency. The
fundamental flux wave and the harmonic flux wave will travel at
synchronous speed in the air gap. This facilitates redistributing the flux
densities in the machine and thereby increasing the total flux per pole in
the machine.
| Inventors:
|
Woodson; Herbert H. (Austin, TX);
Hsu; John S. (Austin, TX)
|
| Assignee:
|
Board of Regents, The University of Texas System (Austin, TX)
|
| Appl. No.:
|
382078 |
| Filed:
|
July 17, 1989 |
| Current U.S. Class: |
318/737; 318/807 |
| Intern'l Class: |
H02P 005/40 |
| Field of Search: |
363/39,43,41
318/730,737,831,832,773-775,812,807
310/184
|
References Cited
U.S. Patent Documents
| 2896143 | Jul., 1959 | Bekey | 318/730.
|
| 3903469 | Sep., 1975 | Ravas.
| |
| 3970914 | Jul., 1976 | Salzmann et al. | 318/812.
|
| 4225914 | Sep., 1980 | Hirata et al. | 363/43.
|
| 4260923 | Apr., 1981 | Rawcliffe.
| |
| 4264854 | Apr., 1981 | Hawtree.
| |
| 4371802 | Feb., 1983 | Morrill.
| |
| 4394596 | Jul., 1983 | Kimura et al.
| |
| 4492890 | Jan., 1985 | MacDonald.
| |
| 4503377 | Mar., 1985 | Kitabayashi et al. | 318/730.
|
| 4508989 | Apr., 1985 | Sawyer et al.
| |
| 4566179 | Jan., 1986 | Sawyer et al.
| |
| 4573003 | Feb., 1986 | Lipo | 318/254.
|
| 4634950 | Jan., 1987 | Klatt | 318/737.
|
| 4795959 | Jan., 1989 | Cooper | 323/308.
|
| 5019766 | May., 1991 | Hsu et al. | 318/807.
|
Other References
Mechler, Robert Carl. "Increased Rating of Polyphase Induction Motors Using
Third Harmonic Excitation," Thesis turned in to The Univ. of Texas at
Austin, May 1985, catalogued Jul. 22, 1985.
Liou, Shy-Shenq Power "Theoretical and Experimental Study of Polyphase
Induction Motors With Added Third Harmonic Excitation," Thesis turned in
to The Univ. of Texas at Austin, Dec. 1985.
|
Primary Examiner: Smith, Jr.; David
Attorney, Agent or Firm: Arnold, White & Durkee
Parent Case Text
This is a continuation of co-pending application Ser. No. 888,818 filed on
Jul. 22, 1986, now abandoned.
Claims
We claim:
1. A method of exciting a polyphase alternating current machine having a
set of windings formed therein wherein at least a first portion of said
winding have a preselected number of poles associated therewith, and at
least a second portion of said windings have an odd multiple preselected
number of poles associated therewith, comprising the steps of:
exciting at least said first portion of the windings of said machine with a
polyphase fundamental frequency current so that a fundamental flux wave
rotates in an air gap of said machine at a speed corresponding to the
frequency of said fundamental frequency current; and
exciting at least said second portion of the windings of said machine with
an odd harmonic frequency of said fundamental frequency current so that a
harmonic flux wave rotates in the air gap of said machine at a speed
substantially synchronous with said fundamental flux wave.
2. The method of claim 1, wherein said machine is excited by a fundamental
frequency current by applying said fundamental frequency current to a
first set of windings, and wherein said machine is excited with an odd
harmonic frequency current by applying said odd harmonic frequency current
to a second set of windings.
3. The method of claim 1, wherein said fundamental frequency current and
said harmonic frequency current are applied to single set of windings.
4. The method of claim 3, wherein the windings in said single set of
windings are connected in a plurality of deltas.
5. The method of claim 4, wherein said deltas are current balanced relative
to one another.
6. The method of claim 4, wherein said deltas are coupled to one another
through transformers.
7. The method of claim 6, wherein one phase of said odd harmonic frequency
current is applied to each leg of one of said deltas.
8. A method of operating an alternating current machine having a set of
windings formed therein wherein at least a first portion of said windings
have a preselected number of poles associated therewith, and at least a
second portion of said windings have an odd multiple preselected number of
poles associated therewith, comprising the steps of:
generating a fundamental flow wave in an air gap of said machine by
exciting at least said first portion of said windings with a fundamental
frequency current; and
generating an odd harmonic flux wave in said air gap of said machine by
exciting at least said second portion of said windings with an odd
harmonic frequency current of said fundamental frequency current, said
harmonic flux wave moving in said air gap in synchronous relation to said
fundamental flux wave.
9. A polyphase alternating current machine having at least one set of
windings formed therein where at least a first portion of said windings
have a preselected number of poles associated therewith, and at least a
second portion of said windings have an odd multiple preselected number of
poles associated therewith, comprising:
means for exciting at least said first portion of said windings with a
polyphase fundamental frequency current to generate a fundamental flux
wave rotating in an air gap of said machine; and
means for exciting at least said second portion of said windings with an
odd harmonic frequency current of said fundamental frequency current to
generate a harmonic flux wave rotating in the air gap of said machine in
synchronous relation with said fundamental flux wave.
10. The method of claim 9, wherein said machine comprises a first set of
windings adapted for being excited by said fundamental frequency current
and a second set of windings adapted for being excited by said odd
harmonic frequency current.
11. An alternating current machine having a set of windings formed therein
wherein at least a first portion of said windings have a preselected
number of poles associated therewith, and at least a second portion of
said windings have an odd multiple preselected number of poles associated
therewith, comprising:
means for generating a fundamental flux wave in an air gap of said machine
by exciting said first portion of said windings with a fundamental
frequency current; and
means for generating a harmonic flux wave in said air gap of said machine
by exciting said second portion of said windings with an odd harmonic
frequency current of said fundamental frequency current, said harmonic
flux wave moving in said air gap in synchronous relation to said
fundamental flux wave.
12. A method for exciting a polyphase alternating current machine to
controllably produce a flux wave of a preselected configuration in an air
gap of said machine, said machine having a set of windings formed therein
wherein at least a first portion of said windings have a preselected
number of poles associated therewith, and at least a second portion of
said windings have an odd multiple preselected number of poles associated
therewith, comprising the steps of:
exciting at least said first portion of said windings with a polyphase
fundamental frequency current so that a fundamental flux wave rotates in
the air gap of said machine at a speed corresponding to the frequency of
said fundamental current;
exciting at least said second portion of said windings with an odd harmonic
frequency of said fundamental frequency current, said odd harmonic
frequency excitation being approximately in phase with said fundamental
frequency current so that an odd harmonic flux wave rotates in the air gap
of said machine at a speed substantially identical to the frequency of
said fundamental flux wave; and
combining said fundamental and harmonic waves to produce a resultant flux
wave having a peak amplitude less than the amplitude of the fundamental
flux wave.
13. A method, as set forth in claim 12, wherein said step of exciting said
machine with a polyphase fundamental frequency current includes applying
said fundamental frequency current to a first set of windings, and wherein
said step of exciting said machine with an odd harmonic frequency includes
applying said odd harmonic frequency current to a second set of windings.
14. A method, as set forth in claim 12, wherein the steps of exciting said
machine with the polyphase fundamental frequency current and the odd
harmonic frequency current includes applying said fundamental frequency
current and said odd harmonic frequency current to a single set of
windings.
15. A method for exciting a polyphase alternating current machine to
controllably produce a flux wave of a preselected configuration in an air
gap of said machine, said machine having a set of windings formed therein
wherein at least a first portion of said windings have a preselected
number of poles associated therewith, and at least a second portion of
said windings have an odd multiple preselected number of poles associated
therewith, comprising the steps of:
generating a fundamental flux wave rotating in the air gap of said machine
at a first preselected speed by exciting at least said first portion of
said windings with a polyphase fundamental frequency current;
generating an odd harmonic flux wave rotating in the air gap of said
machine at said first preselected speed substantially in phase with said
fundamental flux wave by exciting at least said second portion of said
windings with an odd harmonic frequency current of said fundamental
frequency current; and
combining said fundamental and odd harmonic flux waves to produce a
resultant flux wave having a peak amplitude less than the amplitude of the
fundamental flux wave.
16. A method for exciting a polyphase alternating current machine to
controllably produce a flux wave of a preselected configuration in an air
gap of said machine having a set of windings formed therein wherein at
least a first portion of said windings have a preselected number of poles
associated therewith, and at least a second portion of said windings have
an odd multiple preselected number of poles associated therewith,
comprising the steps of:
generating a fundamental flux wave rotating in the air gap of said machine
at a first preselected speed by exciting at least said first portion of
said windings with a polyphase fundamental frequency current;
generating an odd harmonic flux wave rotating in the air gap of said
machine at substantially the same speed as said first preselected speed by
exciting at least said second portion of said windings with an odd
harmonic frequency current of said fundamental frequency current; and
adjusting the phase relationship of said harmonic flux wave relative to
said fundamental flux wave to produce a resultant flux wave having a peak
amplitude less than the amplitude of the fundamental flux wave.
17. An apparatus for exciting a polyphase alternating current machine
having at least one set of stator windings to controllably produce a flux
wave of a preselected configuration in an air gap of said machine, at
least a first portion of said windings having preselected number of poles
associated therewith, and at least a second portion of said windings
having an odd multiple preselected number of poles associated therewith,
comprising:
means for exciting at least the first portion of said windings with a
polyphase fundamental frequency current and generating a resultant
fundamental flux wave rotating in the air gap of said machine at a first
preselected speed;
means for exciting at least the second portion of said windings with an odd
harmonic frequency current of said fundamental frequency current and
generating a resultant odd harmonic flux wave rotating in the air gap of
said machine at said first preselected speed; and
means for adjusting the phase relationship of said harmonic flux wave
relative to said fundamental flux wave to produce a resultant flux wave
having a peak amplitude less than the amplitude of the fundamental flux
wave.
18. An apparatus for exciting a polyphase alternating current machine to
controllably produce a flux wave of a preselected configuration in an air
gap of said machine, having a set of windings formed therein wherein at
least a first portion of said windings have a preselected number of poles
associated therewith, and at least a second portion of said windings have
no odd multiple preselected number of poles associated therewith,
comprising:
means for exciting at least said first portion of said windings with a
polyphase fundamental frequency current so that a fundamental flux wave
rotates in the air gap of said machine at a speed corresponding to the
frequency of said fundamental current;
means for exciting at least said second portion of said windings with an
odd harmonic frequency of said fundamental frequency current, said odd
harmonic frequency excitation being substantially in phase with said
fundamental frequency current so that an odd harmonic flux wave rotates in
the air gap of said machine at a speed corresponding to the frequency of
said fundamental current, said fundamental and harmonic flux waves
combining to produce an air gap resultant flux wave having a peak
amplitude less than the amplitude of the fundamental flux wave.
19. An apparatus for exciting a polyphase alternating current machine
having at least one set of stator windings to controllably produce a flux
wave of a preselected configuration in selected portions of said machine,
at least a first portion of said windings having preselected number of
poles associated therewith, and at least a second portion of said windings
having an odd multiple preselected number of poles associated therewith,
comprising:
a sinusoidal fundamental frequency current source connected to at least
said first portion of said stator windings and adapted for exciting the
windings of said machine to produce a fundamental flux wave rotating about
an air gap in said machine at a speed corresponding to the frequency of
said fundamental frequency;
a sinusoidal odd harmonic frequency current source connected to at least
said second portion of said stator windings and adapted for exciting the
windings of said machine to produce an odd harmonic flux wave rotating
about the air gap of said machine at a speed substantially synchronous
with said fundamental flux wave; and
means for adjusting the phase relation of said odd harmonic current
relative to said fundamental frequency current to produce a resultant flux
wave having a substantially rectangular configuration.
Description
BACKGROUND OF THE INVENTION
The present invention relates generally to methods and apparatus for
improving the performance of alternating current (AC) machines, and more
specifically relates to methods and apparatus for improving the
performance of polyphase AC machines through the injection of harmonic
frequencies into the excitation current.
With conventional polyphase AC machines, both induction and synchronous,
the machines are typically operated by a single frequency source. The
machines have armature windings to which the single frequency sine waves
are applied. The ideal performance of conventional polyphase AC machines
would include a sinusoidal air-gap flux wave of constant amplitude
rotating around the air-gap at synchronous speed. In this theoretical,
ideal polyphase AC machine, the constant amplitude flux wave will produce
a constant electromagnetic torque. The torque of the machine is
monotonically dependent upon this constant amplitude flux wave. This ideal
situation may be approximated in large scale machines.
In conventional AC machines the magnetic flux per pole of the machine is
proportional to the area of 1/2 sine wave of the air-gap flux wave of the
machine. Typically, a conventional AC machine is designed to operate with
at least one of the magnetic members, the iron cores or teeth, of the
machine in flux saturation. In conventional machines, the saturation flux
densities of the iron, or other magnetic members, of the stator and rotor
determine the maximum amplitude of the air-gap flux wave. In conventional
machines, therefore, the amplitude of the fundamental flux sine wave
determines the maximum power output of the machine. This is true even
though maximum use is not made of all of the flux capability of the
magnetic members.
In conventional AC machines, undesirable space harmonics are typically
established in the air-gap flux waves. These naturally-arising space
harmonics occur as a function of the particular machine design when
excited by a fundamental frequency. Factors such as slots in the machines
and core saturation contribute to the generation of these undesirable
space harmonics. These space harmonic flux waves are undesirable because
they typically rotate in the air-gap at speeds other than that at which
the fundamental flux wave rotates. Additionally, the space harmonic flux
waves can be travelling in either a forward or backward direction, as well
as at different speeds, relative to the fundamental flux wave. For
example, a naturally-arising fifth space harmonic flux wave will travel in
a reverse direction relative to the fundamental flux wave and will travel
at 1/5 the speed of the fundamental flux wave. Similarly, a
naturally-arising seventh space harmonic flux wave will travel in the same
direction as the fundamental flux wave, but at 1/7 the speed. These space
harmonic flux waves can interact with the squirrel cage winding in an
induction motor, or with the damper winding in a synchronous motor, to
produce a braking torque which reduces the useful output of the machine.
Additionally, these naturally-generated space harmonic flux waves can
interact with each other, and with the fundamental flux wave, to cause
pulsations in the torque of the machine, as well as unwanted mechanical
vibrations.
Accordingly, the present invention provides a new method and apparatus for
constructing and operating a polyphase AC machine whereby a harmonic flux
wave will travel in the same direction, and at the same (synchronous)
speed, as the fundamental flux wave and whereby the fundamental flux wave
is augmented in response to the harmonic flux wave so as to achieve
improved electromagnetic loading in the magnetic path of the machine; both
achievements serving to improve the useful output of a given machine.
SUMMARY OF THE INVENTION
The methods and apparatus of the present invention improve the performance
of polyphase AC machines through excitation of the machine with
frequencies which are odd harmonics of the fundamental excitation
frequency. This odd harmonic excitation serves to improve performance of
the machine in two ways: (a) the flux distribution caused by the harmonic
excitation enables a greater fundamental flux distribution and thereby
yields an improved total flux distribution in the magnetic path of the
machine, thereby causing improved magnetic loading of the material, and
(b) if the other conductors on the machine (typically on the rotor)
contain conductors or coils responsive to the harmonic frequencies applied
to the armature, or if the pole shape of the rotor produces a permeance
wave responsive to the harmonic frequencies, the harmonic flux
distributions themselves will yield increased torque in the machine.
As will be discussed in more detail later herein, this odd harmonic
excitation can be practiced in a variety of ways, including: separate
coils for fundamental excitation and for each odd harmonic excitation;
multiphase power supplies for both fundamental and harmonic frequencies
coupled to a common winding; the use of a multiplicity of delta-connected
windings coupled to one another through volt-amp balancers, with separate
phases of the harmonic excitation current applied to each delta; and a
common set of delta-connected windings actuated through use of a
multiphase inverter, with a separate phase of the harmonic excitation
current applied to each delta.
BRIEF DESCRIPTION OF THE DRAWINGS
FIGS. 1A-D graphically depict the flux distribution in a section of the
magnetic path of an AC machine. FIG. 1A depicts a sinusoidal flux
distribution. FIG. 1B depicts a square wave flux distribution. FIG. 1C
depicts a total flux distribution achieved by adding an increased level of
fundamental flux distribution with a third harmonic flux distribution.
FIG. 1D depicts a total flux distribution achieved by adding a further
increased fundamental flux distribution with third and fifth harmonic flux
distributions.
FIGS. 2A-C graphically depict the flux distributions in different portions
of an AC machine. FIG. 2A depicts the flux distributions with the machine
operated with neither of the magnetic members in saturation. FIG. 2B
depicts how the flux distributions in a typical low speed machine can be
adjusted through practice of the present invention to improve machine
performance. FIG. 2C depicts how the flux distributions in a typical high
speed machine can be adjusted through practice of the present invention to
improve machine performance.
FIG. 3 graphically depicts the relationship between the ratio of the
fundamental flux density to the maximum design flux density of a machine
and the ratio of the third harmonic flux density to the maximum design
flux density of the machine.
FIG. 4 schematically depicts the phase belts for a machine in accordance
with the present invention having separate windings for fundamental, third
harmonic and fifth harmonic frequencies and power supplies for exciting
such machine.
FIG. 5 schematically depicts a single layer winding for a machine in
accordance with the present invention to be excited through combined
fundamental and third harmonic power sources.
FIG. 6 depicts the power source connections to the machine of FIG. 5.
FIG. 7 schematically depicts a machine in accordance with the present
invention having double layer windings with a per-unit pitch of less than
1.
FIG. 8 depicts the connections and the back emf potential points for a
machine when such machine is excited through use of volt-amp balancers.
FIG. 9 depicts the slot electrical connections for a machine to be excited
as in FIG. 8.
FIG. 10 schematically depicts the connections for the machine of FIGS. 8-9.
FIG. 11 depicts the fundamental frequency back emf voltage differences
between harmonic phases found in alternate slots in the machine of FIGS.
8-10.
FIG. 12 schematically depicts a machine with 60.degree. phase belt
connections for excitation through use of volt-amp balancers.
FIG. 13 schematically depicts the electrical connections for the machine of
FIG. 12.
FIG. 14 schematically depicts the windings of an alternative embodiment of
a machine to be excited through use of volt-amp balancers.
FIG. 15 schematically depicts the connections and the fundamental frequency
back emf potential points for the machine of FIG. 14.
FIG. 16 schematically depicts the electrical connections for the machine of
FIGS. 14 and 15.
FIG. 17 schematically depicts the winding configuration for the armature of
a machine to be excited through use of a multiphase inverter.
FIG. 18 schematically depicts the windings of the machine of FIG. 17.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
The present invention utilizes the injection of harmonic frequencies into
the excitation current of a polyphase AC machine to optimize the flux
densities in both the iron portions and the air-gap of the machine. Those
skilled in the art will recognize that the resulting increase in total
flux in the machine will yield improved performance of the machine.
Referring first to FIGS. 1A-D of the drawings, each Figure graphically
depicts the total flux distribution in a section of the magnetic path of
an AC machine under different conditions. The ordinate of each graph is
the phase angle while the abscissa represents the ratio of the local flux
distribution (B) to the maximum design flux density (B.sub.S) in the
machine.
FIG. 1A depicts a sinusoidal flux distribution 10 in the magnetic path,
resulting from a sinusoidal excitation current. Flux distribution 10 has a
peak amplitude 12. FIG. 1B depicts a square wave flux distribution 14
having an amplitude 16 equal to the peak amplitude 12 of sinusoidal
distribution 10 in FIG. 1A. The theoretical flux per pole of a machine
actuated with the square wave flux distribution 14 of FIG. 1B is 1.57
times the flux per pole of a machine actuated by sinusoidal distribution
10 of FIG. 1A. Such a theoretical machine would make optimal usage of the
flux capacity of the iron portions of the machine. Square waves, however,
cannot be produced in practical machines because practical power supplies
are not available.
A square wave can be synthesized by an infinite set of odd harmonics.
Although such synthesization is impractical, a square wave can be
approximated by a finite set of odd harmonics. FIG. 1C depicts a flux
distribution 18 achieved by adding an increased fundamental flux
distribution 19 to the flux distribution of the third harmonic 20. The
flux per pole of flux distribution 18 is 1.23 times that of the sinusoidal
flux distribution 10 resulting from only fundamental excitation.
FIG. 1D depicts a flux distribution 22 achieved by adding a further
increased fundamental flux distribution 21 to an increased third harmonic
flux distribution 23 and a fifth harmonic flux distribution 24. The flux
per pole of flux distribution 22 is 1.31 times that of sinusoidal flux
distribution 10.
Additional correlated odd harmonic flux distributions will allow further
increases in the relative flux per pole relative to a sinusoidal flux
distribution 10 resulting from fundamental excitation only. The further
addition of these odd harmonic flux distributions will approach the flux
per pole of square wave flux distribution 14. However, additional odd
harmonic flux distributions will yield smaller incremental changes than
those provided by the addition of the third and fifth harmonics as
depicted in FIGS. 1C and 1D. The addition of the third harmonic flux
distribution facilitates the greatest increase in the total flux
distribution and will therefore be discussed here in the greatest detail.
Referring now to FIGS. 2A-C, graphically depicted in each figure are the
core flux distributions 25a, 25b, and 25c in respective figures, and the
teeth and gap flux distributions, 27a, 27b and 27c in respective figures,
in a machine under three different conditions. Conventional practice in
the design of polyphase AC machines is to design the flux densities in the
stator core, the stator teeth, the rotor core and the rotor teeth in such
a way as to avoid excessive flux saturation in any particular section.
This practice serves to limit magnetization current and core loses to
acceptable values. The air-gap flux distribution can be other than a
sinusoidal wave form, distortion in the distribution being largely
dependent upon the degree of saturation in the magnetic paths.
FIG. 2A depicts the core flux distribution 25a, and the teeth and gap flux
distribution 27a of a machine wherein neither section of the machine is
saturated. Each flux distribution is a sinusoid in response to the
fundamental frequency excitation. Core flux distribution 25a is derived
from integration of teeth and gap flux distribution 27a, and is therefore
90.degree. apart in space from teeth and gap flux distribution 27a.
In reality, a machine will be operated with at least one section of the
machine approaching saturation. Further, the degree of saturation in
different magnetic paths cannot be totally equal. For example, in a low
speed machine having a large number of poles, flux densities in the stator
and rotor cores are much lower than the flux densities in the stator and
rotor teeth. The reason is that the minimum dimension of each core is
determined by mechanical requirements, such as rigidity, stress, and
manufacturing requirements; but is not determined by electromagnetic
requirements. Saturation of the teeth is therefore a determining factor
for how much flux per pole can be produced in the machine. Conversely, for
high speed machines, such as two pole machines, the core sections are
typically more saturated than the teeth sections.
The performance, and therefore the rating, of an AC machine is dependent
upon the total flux per pole that can be produced in the machine. The
present invention facilitates the total flux per pole in a polyphase AC
machine to be increased by maintaining or lowering flux density in one
magnetic path while increasing the flux density in another magnetic path.
This redistributing of the flux is accomplished by adjusting the phases of
the harmonic excitation relative to the fundamental excitation. For
example, FIG. 2B depicts exemplary flux distributions contemplated through
use of the present invention in a low speed machine as discussed above.
The density of the core flux 27b is increased through use of fundamental
flux distribution 28 and third harmonic flux 20 distribution 29. At the
same time, however, the density of teeth and gap flux 27b is decreased
relative to fundamental flux distribution 28 and third harmonic flux
distribution 29. The injection of third harmonic excitation current to
establish third harmonic flux distribution 29, therefore, facilitates
increasing the density of the core flux 25b while decreasing the density
of teeth and gap flux distribution 27b, more evenly distributing the flux
in the machine, and, most importantly, facilitating an increase in the
total flux per pole in the machine.
FIG. 2C, depicts exemplary flux distributions contemplated through use of
the present invention with a high speed machine as discussed above. In
FIG. 2C, the phase angle of third harmonic flux distribution 29' has been
changed relative to fundamental flux distribution 28'. This results in a
decrease in the density of core flux 25c and facilitates an increase in
teeth and gap flux 27c. This again promotes a more even flux within the
machine and facilitates an increased total flux per pole in the machine.
Referring now to FIG. 3, therein is graphically depicted, by a curve 31,
the relationship between the fundamental flux density and the third
harmonic flux density in a machine. The abscissa of the graph of FIG. 3
represents the ratio of the fundamental flux density to the maximum design
flux density of a machine, while the ordinate represents the ratio of the
third harmonic flux density to the maximum design flux density of the
machine. The relation expressed in curve 31 assumes that the total flux
density in the machine remains unchanged.
In determining the relative amplitudes for the fundamental and third
harmonic excitation voltages, the maximum third harmonic voltage should be
applied which will facilitate the maximum fundamental voltage which can be
applied which will improve machine performance without exceeding the
thermal rating of the machine. In addition to this primary parameter,
however, the actual ratio between the fundamental and third harmonic
excitation voltages may be affected by secondary factors, such as changes
in core losses due to the excitation by both fundamental and third
harmonic frequencies, or changes in deleterious naturally-occurring space
harmonics as discussed earlier herein, etc. The amplitude and the relative
phases of all excitations will be in sync so as to produce optimal flux
densities as discussed earlier herein.
Following is a discussion of increased performance of different types of AC
machines through use of the present invention. With respect to any of the
below discussed polyphase AC machines, because harmonic sinusoids of
different frequencies are orthogonal, the fundamental and each harmonic of
the stator-produced flux wave will interact to produce torque only with
its counterpart in the rotor produced flux wave.
The benefits of the present invention may be achieved with different types
of AC machines including, for example: squirrel cage induction motors,
wound rotor induction motors, and both salient pole and round rotor
synchronous machines. Different practical considerations with respect to
the present invention will be found with these different machines,
however. A squirrel cage induction motor will experience enhanced torque
production from the increased fundamental component facilitated through
harmonic injection, as depicted in FIGS. 1C and 1D. Additionally, a
squirrel cage induction motor will experience enhanced torque production
from each harmonic flux component provided that the conductors forming the
squirrel cage on the rotor are finely enough divided to allow each space
harmonic of induced current to flow. If the number of bars is so small
that one or more space harmonic currents cannot flow, then no torque can
be produced by those space harmonics in the stator flux wave.
In a wound rotor induction motor, the number of poles produced by rotor
winding is determined by the winding configuration on the rotor. As a
consequence, torque will be produced by each flux component in the
armature for which there is a corresponding winding having a suitable
number of poles on the rotor. For purposes of this discussion, the
armature will have a fundamental winding and one or more harmonic
windings. If the rotor has only a fundamental winding, the machine will
experience enhanced torque from the higher armature fundamental flux
density component as seen in FIGS. 1C and 1D. However, if the rotor
includes windings having the correct number of poles to interact with the
armature harmonic flux distributions, additional torque can be produced by
each of these flux distributions also.
With respect to synchronous machines, torque is produced by the interaction
of fields produced by the armature excitation with the steady fields
produced by direct current in the field winding. The field winding is
typically located on the rotor. Space harmonics in the flux wave produced
by current in the field winding can be produced by properly shaping the
poles in a salient pole machine, or by properly distributing the field
winding in a round-rotor machine. If current in the field winding produces
only a fundamental component of flux density, torque enhancement will
result only from the increased armature fundamental flux component made
possible by the harmonic components in the flux wave. However, for each
harmonic component in the field-produced flux wave which matches a
harmonic in the armature flux wave, further torque enhancement can occur.
In a salient pole synchronous machine, if the salient poles are properly
shaped, then additional torque can be produced by the harmonic components
of the flux wave.
With respect to enhanced performance of any particular machine, any actual
increase in the machine's rating must be determined through examination of
the factors that initially set the rating, i.e., electrical heating of the
armature winding, electrical heating of the rotor winding in an induction
machine, electrical heating of the field winding in a synchronous machine,
core loss heating of the magnetic members, and/or mechanical strength of
machine components.
Flux distributions as depicted in FIGS. 1C or 1D, can be produced by
providing separate sets of polyphase windings for the fundamental and for
each desired harmonic. Each harmonic, thus, may be applied to a discrete
set of windings. Alternatively, and preferably, however, the fundamental
winding will be utilized also for harmonic excitation. This can be done in
a variety of ways. For example, in one method of practicing the present
invention, the outputs of two multiphase power supplies are coupled
together in series to provide fundamental and harmonic excitation of the
fundamental winding. Another method utilizes delta-connected windings
coupled together through volt-amp balancers to balance the potential and
currents of both fundamental and harmonic excitation in the windings. Yet
another alternative method utilizes a single winding with a multiphase
inverter, as often found with adjustable speed devices, to inject the
harmonic excitations onto the fundamental winding.
Referring now to FIG. 4, therein is depicted in schematic form the cross
section of phase belts for a machine 32 for excitation by fundamental,
third harmonic, and fifth harmonic frequencies and the power supplies for
exciting machine 32. Machine 32 is wound with a two-pole, three-phase
fundamental winding 33 which will be excited by fundamental frequency
supply 26. Third harmonic winding 34 is a six-pole, three-phase winding
which will be excited by third harmonic frequency supply 38. Third
harmonic frequency supply 38 will contain phase control circuitry as known
in the art to assure that the third harmonic frequency is maintained in
the desired phase relationship with the fundamental frequency. Fifth
harmonic winding 35 is a ten-pole, three-phase winding which will be
excited by fifth harmonic frequency supply 39 which also contains phase
control circuitry.
A specific phase winding in machine 32 will extend between a pair of
letters in a single winding ring, either 33, 34 or 35, indicated by that
letter and its prime. For example, in the winding schematic the phase
winding extending between a and a' in fundamental winding ring 33 is a
single phase fundamental winding. Similarly, the third harmonic windings a
to a' in winding ring 34 represent third harmonic phase belts. Pairs of
third harmonic windings may be connected either in series or parallel or
may be switched from one connection to the other for ease in starting.
As discussed above, in machine 32 each winding, fundamental winding 33,
third harmonic winding 34 and fifth harmonic winding 35, will be excited
by a separate three phase power supply, 26, 38 and 39, respectively. As
determined above, the frequency of the third harmonic excitation current
will be three times the fundamental frequency, and the frequency of the
fifth harmonic excitation current will be five times that of the
fundamental frequency. The three frequencies will be phase controlled to
be in sync with one another as depicted, for example, in FIG. 1D.
Each harmonic winding must have a number of poles (P.sub.h) equal to:
P.sub.h =np (1)
where:
n is the order of the harmonic (third, fifth, etc.); and
p is the number of poles in the fundamental winding.
For example, for an armature having a fundamental winding having four poles
(p=4), the third harmonic winding must have 3.times.4=12 poles. The
fundamental winding will be excited at the fundamental frequency: .omega.,
and each harmonic winding will be excited at its harmonic of the
fundamental, i.e., a third harmonic winding will be excited at the
electrical frequency, 3.omega.. As will be discussed in more detail later
herein, although the number of phases in the fundamental winding and in
each harmonic winding must be two or more, the number of phases need not
be the same for all windings.
This embodiment allows the greatest flexibility in choosing coil pitches
and numbers of turns for the windings. This construction, however,
requires that an armature slot be occupied by at least two different
windings, thereby resulting in less efficient utilization of the slot
area. Because of the less efficient utilization of the slot area by the
multiple windings, this method typically results in less percentage
improvement than do other methods as will be discussed later herein.
For two-phase systems, the displacement of the fundamental and third
harmonic power supplies are 90 degrees. For three or more phase systems,
displacements of the fundamental and the harmonic frequency supplies are
360/n electrical degrees for n number of phases.
Because the number of poles for the fundamental will automatically
determine the required number of poles for the space harmonic windings, in
a machine where separate windings are provided for the fundamental and for
the harmonic excitation currents, the appropriate number of phases for the
harmonic excitation is determined by the number of slots per pole
available for the harmonic windings. Table 1 indicates the slot
requirements of both fundamental and third harmonic windings for polyphase
machines:
TABLE 1
______________________________________
PH.sub.f
S.sub.pf S.sub.pPHf
PH.sub.3 S.sub.p3
S.sub.pPH3
______________________________________
2 6 3 2 2 1
3 6 2 2 2 1
6 6 1 2 2 1
3 9 3 3 3 l
9 9 1 3 3 1
2 12 6 2 4 2
3 12 4 4 4 1
4 12 3 4 4 1
6 12 2 4 4 1
12 12 1 4 4 1
______________________________________
where:
PH.sub.f indicates the number of phases of the fundamental frequency;
S.sub.pf indicates the slots per pole required for the fundamental winding;
S.sub.pPHf indicates the number of slots per pole per phase for the
fundamental winding;
PH.sub.3 indicates the number of phases of the third harmonic frequency;
S.sub.p3 indicates the number of slots per pole required for the third
harmonic winding; and
S.sub.pPH3 indicates the number of slots per pole per phase for the third
harmonic winding.
Those skilled in the art will recognize that in addition to the integral
slot per pole per phase distributions indicated in Table 1, fractional
slots per pole per phase may be utilized.
As indicated earlier herein, harmonic frequencies may be injected through
use of a single winding for both fundamental and harmonic excitation. FIG.
5 schematically depicts in winding ring 37 a single layer winding for a
four-pole, full pitch machine 36 having 36 slots. Machine 36 will
preferably be excited by balanced nine-phase fundamental current.
Accordingly, as determined by equation 1, machine 36 will have
three-phase, twelve-pole third harmonic excitation. Fundamental windings
are indicated by the pair of a letter and its prime, with a subscript
indicating the slot position of the winding. For example, the winding
between, A, in slot 1, and A', in slot 10, is designated as A.sub.1
-A'.sub.10.
FIG. 6 depicts the power supply connections to the indicated windings of
machine 36 of FIG. 5. Transformer secondaries A-I, indicated as 30a, 30b,
. . . 30i, are the secondaries of one or more transformers coupled to an
appropriate nine-phase fundamental frequency power supply. Those skilled
in the art will recognize that a balanced nine-phase fundamental frequency
supply may be obtained from a three-phase fundamental frequency supply
through use of an appropriate number of transformers; typically, three
transformers, each with four appropriately wound secondaries. Third
harmonic frequency sources x-z, are preferably the secondaries of
transformers 32x, 32y, and 32z, each coupled to one phase of a three-phase
third harmonic frequency power supply. Alternatively, however, the
three-phase third harmonic frequency power supply may coupled directly to
secondaries 30a-30i in the manner indicated. In each arm of the star
connection of FIG. 6, a secondary of the three-phase third harmonic
frequency power supply 32 is coupled between ground and a nine-phase
fundamental frequency supply secondary 30, and to a pair of fundamental
windings. The fundamental windings are identified by the slot numbers of
machine 36 as indicated in FIG. 5. For example, as shown in FIG. 6,
three-phase secondary 32x is coupled in series between ground and
nine-phase secondary 30a. The other side of nine-phase secondary 30a is
then coupled to windings A.sub.1 -A'.sub.10 and to A.sub.19 -A'.sub.28. In
machine 36 of FIGS. 5 and 6, the winding pairs A.sub.1 -A'.sub.10 and
A.sub.19 -A.sub.28 are connected in parallel between nine-phase secondary
30A and ground. Alternatively, winding pairs A.sub.1 -A'.sub.10 and
A.sub.19 -A'.sub.28 may be connected in series with one another between
nine-phase secondary 30a and ground. Such series connection will
approximately double the voltage required by machine 36 while halving the
required current.
Ring 40 in FIG. 5 depicts the third harmonic phasers assigned to each slot
of machine 36. The effective third harmonic excitations shown, (i.e.,
X.sub.1 -X'.sub.4, X.sub.7 -X'.sub.10 ; etc.) do not represent actual
windings, but rather the third harmonic phaser distributions achieved
through application of power as depicted in FIG. 6 to the fundamental
windings arranged as in FIG. 5.
The present invention may also be employed with a multiple layer winding as
opposed to the single layer winding utilized with machine 36 in FIGS. 5
and 6. The winding connections for a machine 42 with a double layer
winding are schematically depicted in FIG. 7. Additionally, the principles
of the present invention may be applied to a machine having less than a
full pitch.
As indicated above, machine 36 of FIGS. 5 and 6 is a four-pole, thirty-six
slot, full-pitch machine. A full-pitch machine is preferable for use with
the present invention because an optimal increase in machine performance
is realized through practice of the invention with a full pitch machine.
However, those skilled in the art will realize that the fundamental
excitation of some full pitch machines is more prone to generate
undesirable fifth and seventh harmonics with such a phase relationship to
the fundamental that machine performance is hindered, as discussed earlier
herein. The coil pitch of a conventional machine is therefore often
designed to be 0.83 so as to minimize these undesirable fifth and seventh
space harmonics.
The fundamental coil pitch factor is determined by the relationship:
cos[(full pitch-actual pitch)/full pitch.times.180/2] (2)
The third harmonic coil pitch factor for a single winding is determined by
the relationship:
cos[(full pitch-actual pitch)/full pitch.times.3.times.180/2](3)
Table 2 indicates the pitch factors for both the fundamental and the third
harmonic for a double layer winding as determined through use of equations
2 and 3.
TABLE 2
______________________________________
Per-Unit Fundamental Pitch
3rd Harmonic
Actual pitch
Pitch Factor Pitch Factor
______________________________________
9 slots 1.00 1.00 1.00
8 slots 0.89 0.98 0.87
7 slots 0.78 0.94 0.50
6 slots 0.67 0.87 0.00
______________________________________
FIG. 7 depicts a 36 slot machine 42 having a four-pole fundamental and a
twelve-pole third harmonic, but with a 0.89 per unit pitch and a double
layer winding. Windings are represented in FIG. 7 in the same manner as
with FIG. 5, i.e., windings are represented by pairs A.sub.1 -A'.sub.9 ;
B.sub.3 -B'.sub.11, etc. Phase windings in adjacent pairs of slots, for
example A.sub.1 -A'.sub.9 and A.sub.2 -A'.sub.10 are connected in
parallel. Inner ring 43 does not represent actual windings of machine 42,
but rather the third harmonic phase distribution of machine 42. Machine 42
may be excited by power connections similar to those depicted in FIG. 6
for machine 36, with the addition of additional connections to the dual
windings in each slot of machine 42.
A third method of practicing the present invention involves the use of
volt-amp balancers. This method allows the use of three-phase power
supplies to provide the fundamental and third harmonic excitation. With
this method the machine windings are delta-connected. Coupled to each
delta is one phase of the three phase third harmonic excitation current.
Each leg of each delta preferably contains the secondary of a transformer
(54a, 54b, 54c; 56a, 56b, 56c; 58a, 58b, 58c in FIG. 10) each of which has
a primary coupled to one phase of the third harmonic frequency power
supply. As previously discussed, the frequency of the third harmonic
excitation current will be three times that of the fundamental excitation
current.
Autotransformers used in the volt-amp balancers of the power connections
for this method will yield variations of resistance and leakage-reactance
between full load on the machine and no load. However, for purposes of
illustration of this embodiment, ideal conditions are assumed, in which
the excitation current, the leakage reactances, and the resistances of
both the volt-amp balancers and the third harmonic transformers are
neglected. Under this assumption, the terminal voltage of a winding is
equal to the back emf produced by the fundamental air-gap flux. These
ideal conditions assumed are generally representative of a no load
condition of a large rating machine, whose no load currents are typically
small compared to their full load currents.
FIG. 8 depicts the connections and the back emf potential points (A.sub.1,
A.sub.2, and A.sub.3) for exciting a machine 45, as depicted in FIG. 9.
Machine 45 is a four-pole, three-phase machine, having 36 slots and
120.degree. phase belts. FIG. 10 schematically depicts the particular slot
electrical connections for the connections depicted in FIG. 8. Inner ring
47 of FIG. 9 depicts the third harmonic phaser distribution of machine 45
when machine 45 is excited through the connections as shown in FIGS. 8 and
10.
With this volt-amp balancer method of harmonic injection, the number of
phases of the third harmonic is determined by the number of slots per
third harmonic pole by means of the relationship:
N.sub.ph3 =the smallest multiplier greater than 1 of [n.sub.s
/(3.times.P.sub.f)] (4)
where:
N.sub.ph3 equals the number of third harmonic phases;
n.sub.s equals the number of slots in the machine; and
P.sub.f equals the number of poles of the fundamental frequency.
In machine 45 coupled as depicted in FIGS. 8 and 10, 120.degree. phase belt
slots 1, 3 and 5, etc. correspond to the three discrete phases of third
harmonic excitation. Each phase of the three-phase third harmonic current
is a zero-sequence current with respect to a particular fundamental delta
winding. The back emfs: emf 1, emf 2, and emf 3, of the fundamental
frequency (in slots 1, 3 and 5, etc.) each have the same amplitude.
Because the phases of these three currents are different, coils in slots
1, 3 and 5, etc. can not be directly connected, either in parallel or in
series.
In the connections of FIG. 8, three volt-amp balancers 49a, 49b, and 49c
are used, one for each phase of the fundamental frequency current. Each
volt-amp balancer is formed of two autotransformers: T1, indicated as 50a,
50b and 50c, and T2, indicated as 52a, 52b and 52c. The turn ratio of
transformers T1 (50a, 50b and 50c), is 1:1. The turn ratio of each
transformer T2 (52a, 52b and 52c), is 2:1. The sides of each transformer
T1 will be connected to a terminal potential point A1 or A3 of first delta
44 or third delta 48, respectively. Autotransformer T2 will be connected
between terminal potential point A2 of second delta 46 and the center tap
53 of its respective transformer T1. Line current of phase A is coupled to
the tap 54a, of autotransformer T2, 52a. Because the turn ratio of
autotransformer T2 is 2:1 relative to tap 54a, the line current of phase A
will convey one portion to terminal A2 of second delta 46 and two portions
into center tap 53a of transformer T1, 50a. Similarly, because the turn
ratio of each autotransformer (T1) 50a, 50b and 50c is 1:1, the current
into the terminal potential point A3 of third delta 48 is the same as that
going into the terminal potential point A1 of first delta 44. Accordingly,
the line currents entering terminal potential points A1, A2 and A3 of
first, second and third deltas 44, 46, and 48, respectively are identical.
As a result, the phase current drive will be identical for each phase.
In operation of the embodiment depicted in FIGS. 8-10, the back emfs at
terminal points A1 and A3 are balanced by transformers (T1) 50a, 50b and
50c. The potential at terminal potential point A2 and at the center tap of
autotransformer T1 are balanced by each auto-transformer T2, 52a, 52b and
52c. As indicated above, each third harmonic current appears as a
zero-sequence current relative to a particular fundamental current.
Accordingly, the volt-amp balancers see only the fundamental frequency
currents and voltages. The back emf voltages are therefore maintained in
the same amplitudes, but in different phases, through operation of
volt-amp balancers 49a, 49b, 49c. The net effect of this connection is
that the flux wave produced is the same as that which would be produced
with the coils of slots 1, 3 and 5 connected in series.
The fundamental frequency back emf voltage difference between the harmonic
phases found in alternate slots, slots 1, 3 and 5, etc., are related as
shown in the vector diagram of FIG. 11. As can be seen in FIG. 11, the
back emfs in each delta 44, 46, 48 are of equal magnitude, but have a
phase angle difference of 40.degree.. The volt-amp balancers balance these
phase differences, which occur between alternate slots in machine 45. As
one skilled in the art can calculate, the total volt-ampere rating of
volt-amp balancers 49a, 49b and 49c, is 0.37 that of the transformers
required to provide the nine-phase fundamental frequency supply discussed
in relation to the system of FIGS. 5 and 6. The results actually achieved
with a machine excited through use of volt-amp balancers will depart
somewhat from the ideal performance shown and described. This departure
will be due in large part to winding resistance and leakage reactance in
the volt-amp balancers and harmonic frequency transformers. Accordingly,
in the design of components for any particular system, the transformers
for the volt-amp balancers and third harmonic excitation should be
designed with sufficiently low winding resistance and leakage reactance to
minimize departure from the ideal.
FIG. 12 depicts another embodiment of this method of harmonic injection
into a four-pole, thirty-six slot machine 60, with windings corresponding
to a 60.degree. phase belt connection. The actual connection diagram for
machine 60 is depicted in FIG. 13. As can be seen in FIG. 13, the polarity
of each third harmonic transformer 61a, 61b, 61c coupled to the delta in
slot 2 is reversed relative to the polarity of third harmonic transformers
63a, 63b, 63c; 65a, 65b, 65c, coupled to the deltas in slots 1 and 3. The
volt-ampere rating of the three volt-amp balancers 62a, 62b and 62c of
FIG. 13 is 0.18 that of the transformers required to provide the
nine-phase supply discussed in reference to the system of FIGS. 5 and 6.
The volt-ampere rating of the balancers is therefore substantially less
even than that of the system of FIGS. 8-10 having 120.degree. phase belt
connections.
Another example of the present invention can be illustrated through use of
an ideal machine having two third harmonic phases. FIG. 14 schematically
depicts a three-phase full-pitch, double layer winding six-pole
fundamental, 36 slot machine 66. Referring to the number of slots per
third harmonic pole is: 36/(3.times.6)=2. Referring to equation 4, because
2 is the smallest multiplier of 2 other than 1, the number of phases of
the third harmonic excitation is 2. Ring 67 depicts the third harmonic
phase distribution for machine 66.
Referring now also to FIGS. 15 and 16, the windings of machine 66 are
connected in two deltas 69, 71. FIG. 15 depicts the winding fundamental
frequency back emf potential points (A1 and A2), corresponding to the
connection of the volt-amp balancers 68a, 68b and 68c of FIG. 17. In the
machine of FIGS. 14-16, the total volt-amp rating of the three volt-amp
balancers is 0.26 that of the transformers which would be needed to supply
the fundamental frequency excitation through use of a three-phase
fundamental frequency supply as discussed in reference to FIGS. 5 and 6.
One phase of the third harmonic excitation will be applied to each leg of
a delta through transformers as depicted at 70 and 72 in FIG. 16.
Because the third harmonic excitation of machine 66 is two phase, one
autotransformer is used for each volt-amp balancer 68a, 68b, 68c. FIG. 16
schematically depicts a detailed connection diagram for exciting machine
66. Each third harmonic frequency supply transformer, 70 and 72, supplies
one of the two phases of the third harmonic excitation current. Each
transformer 70 and 72 preferably includes a single primary and three
equivalent secondaries, coupled in the deltas as shown. As is well known
in the art, because each secondary carries one phase of the fundamental
frequency current, the mmfs of these fundamental frequency currents add to
zero, and no fundamental frequency current is induced in the primary of
the third harmonic transformers. This is true of all third harmonic
transformers in all other embodiments described herein.
A fourth method of injection of third harmonic frequencies utilizes a
single stator winding in conjunction with a multiphase inverter. Referring
now to FIG. 17, therein is schematically depicted a machine 74 having six
fundamental poles in thirty-six slots. The windings of machine 74 will be
connected in two deltas, 78 and 80, displaced 30 electrical degrees from
one another, each to be excited by a three-phase fundamental frequency
supply. Windings indicated by letters enclosed in circles in FIG. 17
represent windings of the second delta as opposed to windings represented
by the unencircled letters. For example winding pair A.sub.1 -A'.sub.7 is
connected in delta 78, while winding A.sub.2 -A'.sub.8 is connected in
delta 80. Ring 75 depicts the distribution of the third harmonic phases in
machine 74.
FIG. 18 schematically depicts machine 74 and a multiphase inverter power
supply 76 suitable for use therewith. In the method of this embodiment,
neither the multiphase power transformers utilized with the apparatus of
FIGS. 5 and 6, nor the volt-amp balancers of the various apparatus of
FIGS. 7-16 are required. Multiphase inverter 76 provides two three-phase
fundamental frequencies 82, 84 each displaced 30.degree. from one another.
The first fundamental frequency outputs 82 are coupled to first delta 78,
while second fundamental frequency outputs 84 are coupled to second delta
80.
The third harmonic excitation is two phase. Each phase is injected into one
of the fundamental delta windings 78, 80. Each leg of each delta, 78, 80,
will include the secondary 86a, 86b, 86c; 88a, 88b, 88c, respectively, of
a transformer having its primary coupled to a third harmonic frequency
supply. Because this multiphase inverter method of the present invention
is particularly suitable for use with adjustable frequency drives, it will
be advantageous to generate the third harmonic frequency directly in
response to the fundamental frequency. This may be done through
conventional means. For example, the rectified power 90 may be applied to
a third harmonic frequency generator 92 outputting two phases 94, 96.
Third harmonic frequency generator 92 will preferably be responsive to one
phase of a fundamental frequency output 98 to enable precise frequency and
phase control of third harmonic frequency phases 94 and 96. Third harmonic
frequency phases 94 and 96 will be coupled to primaries 86', 88' of
transformer secondaries 86a, 86b, 86c: and 88a, 88b, 88c, respectively.
Each of the above-discussed methods and apparatus allows the optimizing of
flux distribution in a polyphase AC machine. As discussed in reference to
FIGS. 1-3, the optimal phase relationship will be selected between the
harmonic excitation current and the fundamental excitation current to
facilitate optimal distribution of the flux density and optional increases
in the total flux per pole of the machine.
Many modifications and variations may be made in the techniques and
structures described and illustrated herein without departing from the
spirit and the scope of the present invention. Accordingly, it is to be
readily understood that the embodiments described and illustrated herein
are illustrative only and are not to be considered as limitations for the
present invention.
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